recursive sequence

hi,i need to find the limit of the following sequencelim (an)1/n n®¥
where an the sequence defined recursively as followsa1=1 and an+1=n(1-lnan) where ln is the natural logatithmI can prove (using induction) that the sequence is increasing and not upper bounded but I don't know how to prove that. I'm sorry but I don't know how to write the sequence in the correct form, so I attached a doc file lim (an)1/n=1 n®¥

In this case may help a preliminary test in order to undestand the behavior of the term $\displaystyle \ln a_{n}$ in (2). Value of $\displaystyle \ln a_{n}$ and $\displaystyle \ln n$ computed till to n=1000 are plotted in figure...